Forcing relations for homoclinic orbits of the Smale horseshoe map.
Formalisme thermodynamique
Formule(s) de Pesin
Fourier expansion along geodesics on Riemann surfaces
For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.
Fractal Newton basins.
Fractalidad extrema e indeterminación clásica en sistemas dinámicos.
Fractions continues hermitiennes et billard hyperbolique
Nous proposons de formaliser une méthode d’approximation diophantienne dans en considérant l’action de sur le demi-plan complexe. On retrouvera le thème classique de la connexion entre développement en fractions continues et flots géodésiques modélisé ici par un billard hyperbolique.
Frame flows on manifolds with pinched negative curvature
From the theorem of Ważewski to computer assisted proofs in dynamics
Generalized Hénon difference equations with delay.
Generate -scroll attractor via composite switching controls.
Generic chaos
Generic diffeomorphisms on compact surfaces
We discuss the remaining obstacles to prove Smale's conjecture about the C¹-density of hyperbolicity among surface diffeomorphisms. Using a C¹-generic approach, we classify the possible pathologies that may obstruct the C¹-density of hyperbolicity. We show that there are essentially two types of obstruction: (i) persistence of infinitely many hyperbolic homoclinic classes and (ii) existence of a single homoclinic class which robustly exhibits homoclinic tangencies. In the course of our discussion,...
Generic linear cocycles over a minimal base
We prove that a generic linear cocycle over a minimal base dynamics of finite dimension has the property that the Oseledets splitting with respect to any invariant probability coincides almost everywhere with the finest dominated splitting. Therefore the restriction of the generic cocycle to a subbundle of the finest dominated splitting is uniformly subexponentially quasiconformal. This extends a previous result for SL(2,ℝ)-cocycles due to Avila and the author.
Generic measures for geodesic flows on nonpositively curved manifolds
We study the generic invariant probability measures for the geodesic flow on connected complete nonpositively curved manifolds. Under a mild technical assumption, we prove that ergodicity is a generic property in the set of probability measures defined on the unit tangent bundle of the manifold and supported by trajectories not bounding a flat strip. This is done by showing that Dirac measures on periodic orbits are dense in that set.In the case of a compact surface, we get the following sharp result:...
Generic properties of closed geodesics on smooth hypersurfaces.
Generic Properties of Geodesic Flows.
Généricité d'exposants de Lyapunov non-nuls pour des produits déterministes de matrices
Geodätischer Fluß auf Mannigfaltigkeiten vom hyperbolischen Typ.
Geodesic Flow on SO(4) and Abelian Surfaces.